Reboot log App

Could someone make a simple app that logs each time a phone reboots? Something that runs in the background and starts with WP8 and simply creates a list with Date and time of the last reboot. A list in pages so we screenshot each page and email it to manufacturers. That could be very useful to WP8 users to document WP8 rebooting on its own. Of course, added functionality could be of use, like anything you can read during the reboot and add to the log file. Or a build in, export list as pictures. I hope someone does this! We need to get the bugs worked out of all WP8 devices!